Problem: Simplify the following expression: $n = \dfrac{-42y^3 + 56y^2}{-28y^3 + 77y^2}$ You can assume $y \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-42y^3 + 56y^2 = - (2\cdot3\cdot7 \cdot y \cdot y \cdot y) + (2\cdot2\cdot2\cdot7 \cdot y \cdot y)$ The denominator can be factored: $-28y^3 + 77y^2 = - (2\cdot2\cdot7 \cdot y \cdot y \cdot y) + (7\cdot11 \cdot y \cdot y)$ The greatest common factor of all the terms is $7y^2$ Factoring out $7y^2$ gives us: $n = \dfrac{(7y^2)(-6y + 8)}{(7y^2)(-4y + 11)}$ Dividing both the numerator and denominator by $7y^2$ gives: $n = \dfrac{-6y + 8}{-4y + 11}$